Related papers: Evaluating Error Bound for Physics-Informed Neural…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

Fractional differential equations are powerful mathematical descriptors for intricate physical phenomena in a compact form. However, compared to integer ordinary or partial differential equations, solving fractional differential equations…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

We consider the evolution of linear matter perturbations in the context of the standard cosmological model ($\Lambda$CDM) and a phenomenological modified gravity model. We use the physics-informed neural network (PINN) bundle method, which…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann electrostatics. These problems are characterized by sharp…

We propose a new loss function for supervised and physics-informed training of neural networks and operators that incorporates a posteriori error estimate. More specifically, during the training stage, the neural network learns additional…

We propose a physics-informed quantum algorithm to solve nonlinear and multidimensional differential equations (DEs) in a quantum latent space. We suggest a strategy for building quantum models as state overlaps, where exponentially large…

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…

A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…

This paper introduces for the first time, to our knowledge, a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments…

Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

In recent times machine learning methods have made significant advances in becoming a useful tool for analyzing physical systems. A particularly active area in this theme has been "physics-informed machine learning" which focuses on using…